A deterministic annealing (DA)-based expectation-maximisation (EM) algorithm is proposed for robust learning of Gaussian mixture models. By combing the DA approach, trimmed likelihood function and Bayesian information criterion (BIC), the proposed algorithm can simultaneously perform model selection and outlier detection, and mitigate the problems of local optima and boundary of parameter space with the conventional EM algorithm. Experiments demonstrate that the proposed algorithm can determine the number of components correctly even though the data are contaminated by outliers.